How to Simplify Variable Expressions

Learn the definition of variable and expression and how to simplify variable expressions.

Step by step guide to simplifying variable expressions

• In algebra, a variable is a letter used to stand for a number. The most common letters are: \(x, y, z, a, b, c, m\) and \(n\).
• An algebraic expression is an expression contains integers, variables, and math operations such as addition, subtraction, multiplication, division, etc.
• In an expression, we can combine “like” terms. (values with same variable and same power)

Simplifying Variable Expressions – Example 1:

Simplify this expression. \(2 \ x \ + \ 3 \ x \ + \ 4=\)?

Solution:

Combine “like” terms. Then: \(2 \ x \ + \ 3 \ x \ = 5 \ x \) (remember you cannot combine variables and numbers).

Then: \(2 \ x \ + \ 3 \ x \ + \ 4=5 \ x \ + \ 4\) (remember you cannot combine variables and numbers).

Simplifying Variable Expressions – Example 2:

Simplify this expression. \(12 \ – \ 3 \ x^{2} \ + \ 5 \ x \ + \ 4 \ x^{2}=\)?

Solution:

Combine “like” terms. \(- \ 3 \ x^{2} \ + \ 4 \ x^{2}=x^{2}\)
Then: \(12 \ – \ 3 \ x^{2} \ + \ 5 \ x \ + \ 4 \ x^{2}\) \(=12 \ + \ x^2 \ + \ 5 \ x\). Write in standard form (biggest powers first): \(x^2 \ + \ 5 \ x \ + \ 12\)

Simplifying Variable Expressions – Example 3:

Simplify this expression. \((10x+2x+3)=\)?

Solution:

Combine “like” terms. Then: \((10x+2x+3)=12x+3\) (remember you cannot combine variables and numbers).

Simplifying Variable Expressions – Example 4:

Simplify this expression. \(12-3x^2+9x+5x^2=\)?

Solution:

Combine “like” terms: \(-3x^2+5x^2=2x^2\)
Then: \(12-3x^2+9x+5x^2=12+2x^2+9x\). Write in standard form (biggest powers first): \(2x^2+9x+12\)

Exercises for Simplifying Variable Expressions

Simplify each expression.

• \(\color{blue}{– 2 – x^2 – 6x^2}\)
• \(\color{blue}{ 3 + 10x^2 + 2}\)
• \(\color{blue}{ 8x^2 + 6x + 7x^2}\)
• \(\color{blue}{5x^2 – 12x^2 + 8x }\)
• \(\color{blue}{– 2(4 – 6x) – 3x }\)
• \(\color{blue}{ 9 – 2x + 5x + 2}\)

Download Simplifying Variable Expressions Worksheet

Answers

• \(\color{blue}{– 7x^2 – 2}\)
• \(\color{blue}{10x^2 + 5}\)
• \(\color{blue}{15x^2 + 6x}\)
• \(\color{blue}{– 7x^2 + 8x}\)
• \(\color{blue}{9x \ – 8 }\)
• \(\color{blue}{3x \ + 11}\)